Eevee vs Cycles Blender 2.8 & Glossy BSDF [SOLVED - FIX IT]
In the Render properties at the right-hand side of the screenshot you can see the Screen Space Reflections section - enable that and you should see reflections.

Eevee works quite differently to Cycles and the more features are enabled the slower the render. Many of the options are disabled by default for efficiency and must be specifically enabled when needed.